$3 n^2+2 n-4-2 n^2-2 n+12=$
Answer (1)
Combine the n 2 terms: 3 n 2 − 2 n 2 = n 2 .
Combine the n terms: 2 n − 2 n = 0 .
Combine the constant terms: − 4 + 12 = 8 .
The simplified expression is n 2 + 8 .
Explanation
Understanding the Problem We are given the expression 3 n 2 + 2 n − 4 − 2 n 2 − 2 n + 12 and we want to simplify it by combining like terms. This involves grouping terms with the same power of n and constant terms.
Combining n^2 Terms First, let's group the n 2 terms: 3 n 2 − 2 n 2 = ( 3 − 2 ) n 2 = 1 n 2 = n 2 .
Combining n Terms Next, let's group the n terms: 2 n − 2 n = ( 2 − 2 ) n = 0 n = 0 .
Combining Constant Terms Now, let's group the constant terms: − 4 + 12 = 8 .
Final Simplification Finally, we combine the simplified terms: n 2 + 0 + 8 = n 2 + 8 . Therefore, the simplified expression is n 2 + 8 .
Examples
Imagine you are designing a rectangular garden where the area is represented by the expression 3 n 2 + 2 n − 4 . Later, you decide to reduce the size of the garden, and the reduction in area is represented by 2 n 2 + 2 n − 12 . To find the new area of the garden, you subtract the reduction from the original area: ( 3 n 2 + 2 n − 4 ) − ( 2 n 2 + 2 n − 12 ) . Simplifying this expression gives you the new area, which is n 2 + 8 . This shows how simplifying algebraic expressions can help in practical situations like garden design or any scenario involving area calculations.
